diff --git a/docs/02advanced/04recursion/index.mdx b/docs/02advanced/04recursion/index.mdx
index bd6a0b768..28e5a1800 100644
--- a/docs/02advanced/04recursion/index.mdx
+++ b/docs/02advanced/04recursion/index.mdx
@@ -214,13 +214,21 @@ $$
 
 <Answer>
 
-ユークリッドの互除法を用いれば簡単にできます。
+ユークリッドの互除法を用いれば簡単にできます。$\mathrm{gcd}(a, b)$ を $a$ と $b$ の最大公約数とします。
 
 例：$30$ と $18$ の最大公約数を求める。
 
-- $30$ を $18$ で割った余りは、$12$
-- $18$ を $12$ で割った余りは、$6$
-- $12$ を $6$ で割った余りは、$0$
+$$
+\begin{align*}
+    \mathrm{gcd}(30, 18) &= \mathrm{gcd}(18, 30 - 18\times 1) \\
+                         &= \mathrm{gcd}(18, 12) \\
+                         &= \mathrm{gcd}(12, 18 - 12\times 1) \\
+                         &= \mathrm{gcd}(12, 6) \\
+                         &= \mathrm{gcd}(6, 12 - 6\times 2) \\
+                         &= \mathrm{gcd}(6, 0) \\
+                         &= 6
+\end{align*}
+$$
 
 よって、最大公約数は $6$
 
@@ -228,6 +236,30 @@ $$
 
 <ViewSource path="/recursion/gcd.ipynb" />
 
+:::note
+
+このプログラムは、はじめの引数が $a < b$ の場合でも動きます。一度目の再帰で、`gcd(b, a % b)` = `gcd(b, a)` が返されるからです。
+
+つまり、$18$ と $30$ の最大公約数を求めるとき、
+
+$$
+\begin{align*}
+    \mathrm{gcd}(18, 30) &= \mathrm{gcd}(30, 18 - 30\times 0) \\
+                         &= \mathrm{gcd}(30, 18) \\
+                         &= \mathrm{gcd}(18, 30 - 18\times 1) \\
+                         &= \mathrm{gcd}(18, 12) \\
+                         &= \mathrm{gcd}(12, 18 - 12\times 1) \\
+                         &= \mathrm{gcd}(12, 6) \\
+                         &= \mathrm{gcd}(6, 12 - 6\times 2) \\
+                         &= \mathrm{gcd}(6, 0) \\
+                         &= 6
+\end{align*}
+$$
+
+となります。
+
+:::
+
 また、最大公約数 $\mathrm{gcd}(a, b)$ と最小公倍数 $\mathrm{lcm}(a, b)$ の間には次のような関係があります。
 
 $$
diff --git a/static/practice/gcd_recursive.ipynb b/static/practice/gcd_recursive.ipynb
index 93ae103e0..854788675 100644
--- a/static/practice/gcd_recursive.ipynb
+++ b/static/practice/gcd_recursive.ipynb
@@ -7,12 +7,10 @@
    "metadata": {},
    "source": [
     "def gcd(a, b):\n",
-    "    if a < b:\n",
-    "        a, b = b, a\n",
-    "    if b != 0:\n",
-    "        return gcd(b, a % b)\n",
-    "    else:\n",
+    "    if b == 0:\n",
     "        return a\n",
+    "    else:\n",
+    "        return gcd(b, a % b)\n",
     "\n",
     "\n",
     "print(gcd(12, 16))"
diff --git a/static/recursion/gcd.ipynb b/static/recursion/gcd.ipynb
index f82d3c6ab..3f6dbf432 100644
--- a/static/recursion/gcd.ipynb
+++ b/static/recursion/gcd.ipynb
@@ -7,8 +7,6 @@
       "metadata": {},
       "source": [
         "def gcd(a, b):\n",
-        "    if a < b:\n",
-        "        a, b = b, a\n",
         "    if b == 0:\n",
         "        return a\n",
         "    else:\n",
diff --git a/static/recursion/lcm.ipynb b/static/recursion/lcm.ipynb
index 294be73ec..acf72f8a3 100644
--- a/static/recursion/lcm.ipynb
+++ b/static/recursion/lcm.ipynb
@@ -6,17 +6,15 @@
     {
       "metadata": {},
       "source": [
-        "def gcd(m, n):\n",
-        "    if m < n:\n",
-        "        m, n = n, m\n",
-        "    if n == 0:\n",
-        "        return m\n",
+        "def gcd(a, b):\n",
+        "    if b == 0:\n",
+        "        return a\n",
         "    else:\n",
-        "        return gcd(n, m % n)\n",
+        "        return gcd(b, a % b)\n",
         "\n",
         "\n",
-        "def lcm(m, n):\n",
-        "    return m * n / gcd(m, n)\n",
+        "def lcm(a, b):\n",
+        "    return a * b / gcd(a, b)\n",
         "\n",
         "\n",
         "print(lcm(30, 18))"